MOSCOW—Russia will see the largest capital outflow since the 2008 financial crisis in the first quarter of this year, the country's deputy economy minister said Monday, as relations with the West have sharply deteriorated since Moscow annexed Crimea this month.

Capital outflow in the first three months of 2014 will reach between $65 billion and $70 billion, Andrei Klepach said, slightly higher than for the whole of last year, and the...